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Bayesian Gaussian Process Optimization can be considered as a method of the determination of the model parameters, based on the experimental data. In the range of soft QCD physics, the processes of hadron and nuclear interactions require…
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…
We consider the {\em mobile facility location} (\mfl) problem. We are given a set of facilities and clients located in a common metric space. The goal is to move each facility from its initial location to a destination and assign each…
Due to the dynamic nature of financial markets, maintaining models that produce precise predictions over time is difficult. Often the goal isn't just point prediction but determining uncertainty. Quantifying uncertainty, especially the…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…
We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…
This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…
An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to…
We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…
We discuss the statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has…
We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities…
Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati, we provide a general technique to compare the tail of a given random variable to that of a reference distribution. This enables us to give concrete conditions to…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…
Random forests have proven to be reliable predictive algorithms in many application areas. Not much is known, however, about the statistical properties of random forests. Several authors have established conditions under which their…
Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and…
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…